The use of high dose chemoradiotherapy followed by marrow transplantation can cure some patients of malignant lymphoma after they have failed conventional chemotherapy. In this project we propose to determine more precisely the curability of patients transplanted for malignant lymphoma at first relapse or second remission. We will investigate the influence of disease histology and allogeneic marrow on treatment outcome. Patients with a prior history of radiotherapy to the chest are at high risk to develop interstitial pneumonitis after our standard CY-TBI regimen, and for this group we propose to test a chemotherapy- only preparative regimen. Other new preparative regimens (as outlined in sections I.A. and I.B.) will be tested in patients transplanted for refractory disease. Finally, we will compare prospectively marrow transplantation to the best available salvage chemotherapy in patients who have relapsed after first line chemotherapy.